The Accounting of Entropy Production in Humans and Ecosystems Entropy as an Indicator

Recently, entropy production in living systems, such as humans and ecosystems, has been calculated in order to investigate a general hypothesis on entropy production in the process of development, growth, and aging of organisms and ecosystems. Entropy and its derived functions are thus being used as a measure of performances and/or state of health of a system.

Ichiro Aoki calculated entropy production in the human body as a whole from observed energetic data. This method is applied in order to give information about the trend of entropy production in humans over human life span. As a result, a two-stage character is observed: an early increasing stage and a later decreasing stage until death (Figure 2).

Similar methods for calculating entropy production have been applied by Aoki and Ludovisi and Paoletti to lake ecosystems.

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Figure 2 Entropy production per human individual versus years of age (0-75) for male and female. x represents male; and o represents female. Reproduced from Aoki I (1995) Entropy production in living systems: From organisms to ecosystems. Thermochimica Acta 250: 359-370, with permission from Elsevier.

Later stage

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Figure 2 Entropy production per human individual versus years of age (0-75) for male and female. x represents male; and o represents female. Reproduced from Aoki I (1995) Entropy production in living systems: From organisms to ecosystems. Thermochimica Acta 250: 359-370, with permission from Elsevier.

In the case studies presented in literature, the entropy balance corresponds to the change in entropy content of a lake with the net amount of entropy inflow minus entropy outflow. In other words, entropy variations have been assessed corresponding to energy flows such as: Eabs, short-wave solar energy absorbed by the surface; Erf, reflected long-wave infrared radiation; Eev, evaporation heat loss; Eatm, atmosphere-water heat exchange; Er, rain precipitation (corresponding heat flow); Eef, outgoing water flow through effluents (corresponding heat flow); Ewl, water withdrawal and other water losses (corresponding heat flow); En, other nth factor. Thus the entropy balance is expressed in the same form as eqn [8] presented above.

The assessment of the entropy variation due to exchanges with the external environment of a lake ecosystem results in

while the entropy variation due to internal processes is given by the change in entropy content of the lake:

where aQ^is the change of the heat storage, and Tw is the mean temperature of the lake water.

Thus the entropy production for a lake ecosystem is calculated by

where aSe is the net incoming entropy flow into the lake.

Later stage

Time

Figure 3 A hypothetical entropy principle for living systems. Scales are arbitrary.

Time

Figure 3 A hypothetical entropy principle for living systems. Scales are arbitrary.

Findings from the entropy production assessment show that processes of ecological succession (evolution) in a lake accompany the increase in entropy production, always proceeding from oligotrophy to eutrophy. Results obtained by applying this method to specific lake ecosystems show an overall trend in ecological succession: entropy production increases with time in an early stage (growing stage) of succession, is kept almost stationary in an intermediate stage, and decreases in a later stage (senescent stage) of ecological succession. Eutrophication in a lake is an irreversible process; hence, from the above entropy principle for eutrophication, the entropy production in a lake increases with time. This situation is parallel to the trend in the early stage of the human life span. In this respect, the ecosystem may be regarded as a 'super-organism' and, conversely, the organism as a 'mini-ecosystem'. Experiments for various organisms and ecosystems by the use of an entropy production balance, can be further examined in order to propose a hypothesis about the entropy principle, stated by the second law of thermodynamics, for living systems, that are open and far from equilibrium systems: entropy production in a living system consists of two or more phases: an early increasing stage, a later decreasing stage, and an intermediate stage. This is shown schematically in Figure 3.

The early increasing stage is the phase of development and growth of the systems, the later decreasing stage is the phase of senescence, and the intermediate stage is the transitional or stationary one.

Entropy has also been used as a more general indicator to assess the sustainability of ecosystems under artificial external forcing. By using the 'entropy pump' hypothesis, Yuri Svirezhev tries to calculate the entropy production for the ecosystems under anthropogenic stress in order to give a measure of environmental degradation under anthropogenic impact. An example of this application is the sustainability assessment of an agroecosystem, the latter considered to be a transformer of the input flow of artificial energy into the output flow of agricultural production. In this case entropy is used in its original meaning, that is, as a measure of degradation: calculating the overproduction of entropy of a certain process can give a measure of the sustainability of the process itself. The transition from natural to anthropogenic ecosystem is usually performed sufficiently fast that an entropy overproduction is expected to be compensated by the outflow of entropy to the environment. This compensation can occur at the expense of environmental degradation, resulting, for instance, from heat and chemical pollution, and mechanical impact on the system. Starting from eqn [8] and following this approach, Svirezhev, formulated a general entropy balance for the annual total rate of entropy for an agroecosystem:

where T is the mean temperature of a vegetation period and W is the annual inflow of artificial energy. XP; is a part of the annual gross agroecosystem production, which remains on the field and P0 is the reference ecosystem (in this case, a grassland) annual gross primary production. From eqns [8] and [16] it follows that diS = (W + XP1)/T and deS = -P0/T. A deeper analysis of eqn [16] permits to relate W and P1 with appropriate coefficients which take into account the entropy contribution for every single process, such as soil erosion, chemical pollution, acidification of soil, chemical contamination by pesticides and fertilizers, and other intermediate variants.

It is evident that if u >0, then a system accumulates entropy and it destroys its environment, that is, ceases to be sustainable. In such way it is possible to find a critical value of artificial inflow energy (Wcr) for which degradation overcomes sustainability, and decomposing W in its contributing parts it is possible to tune the management of an agroecosystems toward less environmental impact. Finally, this approach helps to better understand the 'entropy fee', which mankind pays for high crop yield and for the intensification of agriculture. In the framework of this approach, the variety of all the processes inside an agroecosystem is reduced to the one process of heat production and dissipation. The entropy production results by the total thermal effect of different physical and chemical processes taking place in the system. This very serious simplification of an agriculture system only conceived as a physical one, is obviously very reductive in a biological realm.

Eric Schneider and James Kay have studied the thermo-dynamic development of natural systems and explain things in terms of macroscopic behavior of energy processing, suggesting that biological systems develop in a manner as to increase their degradation rate. In this sense the development of ecosystem maturity via succession is the result of self-organization processes addressed to maximize incoming energy dissipation rates throughout each stage of succession. For example, a tendency toward higher respiration and transpiration, larger ecosystem biomass and higher diversity results in more and different pathways for energy degradation. This tendency is known as the 'maximum energy dissipation principle' which affirms that as ecosystems grow and develop, they increase their total dissipation, that is, their entropy production. The development of self-organization is therefore a mean of dissipating gradients imposed on systems; thus biological growth, ecosystem development, and evolution represent the development of new dissipa-tive pathways. In this vision, life is a balance between the imperatives of survival (by developing the most power inflow and using it to best meet needs for survival, as in the Lotka principle) and energy degradation.

However, this principle seems in contrast with the findings presented above about entropy production trends in humans and ecosystems. Since the increasing trend of entropy production follows the increasing trophic state in lake ecosystems, maximum entropy production is expected during intermediate stages of development of a community (that of phytoplankton in lake ecosystems) in a growth phase season, when organisms are accomplishing the colonization of an unexploited environment, before the achievement of the climax state.

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